Solve for $r$: $r = \displaystyle\frac{\sqrt{5^2+12^2}}{\sqrt{16+9}}$. Express as a common fraction.
Solution: We have  \[r = \displaystyle\frac{\sqrt{5^2+12^2}}{\sqrt{16+9}} = \frac{\sqrt{25+144}}{\sqrt{25}} = \frac{\sqrt{169}}{5} = \boxed{\frac{13}{5}}.\]